TRANSIENT ANALYSIS OF ROTOR DISC OF DISC BRAKE USING ANSYS doc/IJMIE_AUGUST2012/IJMRA-MIE1626.pdf · TRANSIENT ANALYSIS OF ROTOR DISC OF DISC BRAKE USING ANSYS V.M.M.Thilak* _____

IJMIE Volume 2, Issue 8 ISSN: 2249-0558 ___________________________________________________________

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International Journal of Management, IT and Engineering http://www.ijmra.us

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August 2012

TRANSIENT ANALYSIS OF ROTOR DISC OF DISC

BRAKE USING ANSYS

V.M.M.Thilak*

__________________________________________________________

Abstract

Transient Thermal and Structural Analysis of the Rotor Disc of Disk Brake is aimed at

evaluating the performance of disc brake rotor of a car under severe braking conditions and there

by assist in disc rotor design and analysis. An investigation into usage of new materials is

required which improve braking efficiency and provide greater stability to vehicle. This

investigation can be done using ANSYS software. ANSYS is a dedicated finite element package

used for determining the temperature distribution, variation of the stresses and deformation across

the disc brake profile. In the present work, an attempt has been made to investigate the suitable

hybrid composite material which is lighter than cast iron and has good Young’s modulus, Yield

strength and density properties. Aluminum base metal matrix composite and High Strength Glass

Fiber composites have a promising friction and wear behavior as a Disk brake rotor. The transient

thermo elastic analysis of Disc brakes in repeated brake applications has been performed and the

results were compared. The suitable material for the braking operation is S2 glass fiber and all the

values obtained from the analysis are less than their allowable values. Hence the brake Disc

design is safe based on the strength and rigidity criteria. By identifying the true design features,

the extended service life and long term stability is assured.

* Assistant Professor/ Mechanical Engineering, S.N.S.College of Engineering- Coimbatore-

641107.




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1. Introduction

A disc brake consists of a cast iron disc bolted to the wheel hub and a stationary

housing called caliper. The caliper is connected to stationary part of the vehicle like the axle

casing or the stub axle as is cast in two parts each part containing a piston. In between each piston

and the disc there is a friction pad held in position by retaining pins, spring plates etc. passages

are drilled in the caliper for the fluid to enter or leave each housing.Each cylinder contains rubber-

sealing ring between the cylinder and piston.The principle used is the applied force acts on the

brake pads, which comes in to contact with the moving disc. At this point of time due to friction

the relative motion is constrained.

Sok Won Kim [15] investigated the temperature distribution, the thermal deformation,

and the thermal stress of automotive brake disks have quite close relations with car safety;

therefore, much research in this field has been performed.Xiangie Meng [5] based on the review

of researches on the vibration and noise related to automobile brake, the four degrees of freedom

nonlinear dynamics model of brake disk and pads is established, the stability of vibration system

at the equilibrium points is analyzed.The main idea is to express the thermal energy that the disc

stores when abraking action is performed. Inorder to express this energy, the global system that

influences the slowing down of the vehicle has to be considered.

This system is composed by the following technical braking components: brake discs,

transmission retarders, controlled engine brakes and exhaust brakes.Jadon [15]carries out a

transient analysis for the thermo elastic contact problem of the disk brakes with heat generation is

performed using the finite element analysis. To analyze the thermo elastic phenomenon occurring

in the disk brakes, the occupied heat 12 conduction and elastic equations are solved with contact

problems.

2. Finite Element Analysis

The finite element method has become a powerful tool for the numerical solutions of a

wide range of engineering problems. The present study is based on the coupled theory in which

temperatures and displacements are mutually influenced. If the solution is known at time t, the

solution for next time step t+ Δt needs the information of Rt+Δt

on the right hand side. However,




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the distributions of pressure P on the friction surfaces at this time step, which appear in the

thermal boundary conditions, are unknown. When solving the frictional contact problems in time

domain, Zagrodzki [19] assumed the contact pressure P to be the change in time of the

Total force represented by the applied hydraulic pressure P of the known time function as

follows:

However, the solution using the assumption of Eq.(3.17) are generally reasonable in case

of the variation in time of contact area or specially, the drag braking condition(constant hydraulic

pressure Ph

).Consequently, for the frictional contact problems where the time evolution of contact

pressure is important, the fully implicit scheme should be used. The numerical simulation for the

coupled transient thermo elastic contact problem is carried out in the following way: At time t, it

is assumed that the temperature distribution is T is given. Using this temperature, the thermal load

vector PΔΤ

can be obtained. To solve the contact problem, elastic is iteratively calculated to satisfy

the no overlap condition and the equilibrium state on the contact surface. As a result of this

calculation, new pressure distribution and new contact conditions on the contact surfaces can be

obtained. Then, using new heat flux vector R constructed from relation and new contact

conditions, the heat and elastic can be solved at time t + Δ t . The fully implicit transient iteration

is repeated to calculate the equilibrium state of the coupled thermo elastic equations at every time

step. In this way, the solution of thermo elastic state at any time could be obtained.

3. Materials used for Rotor Disc:

3.1 Cast Iron:

Cast iron usually refers to grey cast iron, but identifies a large group of ferrous alloys,

which solidify with a eutectic. Iron accounts for more than 95%, while the main alloying elements

are carbon and silicon. The amount of carbon in cast iron is the range 2.1-4%, as ferrous alloys

with less are denoted carbon steel by definition. Cast irons contain appreciable amounts of silicon,

normally 1-3%, and consequently these alloys should be considered ternary Fe-C-Si alloys. Here




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graphite is present in the form of flakes. Disc brake discs are commonly manufactured out of a

material called grey cast iron.

3.2 Aluminum based Metal MatrixComposites:

Metal composite materials have found application in many areas of daily life for quite

some time. Materials like cast iron with graphite or steel with high carbide content, as well as

tungsten carbides, consisting of carbides and metallic binders, also belong to this group of

composite materials. Substantial progress in the development of light metal matrix composites has

been achieved in recent decades, so that they could be introduced into the most important

applications.

3.3 E-Glass Fiber:

The use of E-Glass as the reinforcement material in polymer matrix composites is

extremely common. Optimal strength properties are gained when straight, continuous fibers are

aligned parallel in a single direction. To promote strength in other directions, laminate structures

can be constructed, with continuous fibers aligned in other directions. E-Glass is a low alkali glass

with a typical nominal composition of SiO2

54wt%, Al2O

3 14wt%, CaO+MgO 22wt%, B

2O

3

10wt% and Na2O+K

2O less than 2wt%.These involve melting the glass composition into a

platinum crown which has small holes for the molten glass to flow. Continuous fibers can be

drawn out through the holes and wound onto spindles, while short fibers may be produced by

spinning the crown, which forces molten glass out through the holes centrifugally. Fibers are cut

to length using mechanical means or air jets.

3.4 S2 Glass Fiber:

High-strength glass fibers are used in applications requiring greater strength and lower

weight. High-strength glass is generally known as S-type glass in the United States, R-glass in

Europe and T-glass in Japan. S-glass was originally developed for military applications in the

1960s, and a lower cost version, S-2 glass, was later developed for commercial applications. The

most traditional composites that fall within the fiber reinforced plastic composites almost

inherently are produced using E-glass fiber. And we tend to think that most advanced composites

are manufactured for high strength performance using S-2 glass fiber materials. Silicon dioxide




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(SiO2

) is the one of the primary ingredients in both sand and glass fiber, there are a wide number

of other ingredients mixed into the system during processing .

PROPERTIES Cast Iron AlMMC S2 glass E glass

DENSITY, ρ 7100

Kg/m3

2765.2

Kg/m3

2460 2580

YOUNGS

MODULUS,E 125 GPa 98.5 GPa 86.9 Gpa 72.3

THERMAL

CONDUCTIVITY,

k

54 W/m.K 181.65

W/m.K

1.45

W/m.K

1.3

W/m.K

SPECIFIC HEAT.

Cp

586

J/Kg.K

836.8

J/Kg.K

737

J/Kg.K

810

J/Kg.K

POSSION’S

RATIO, υ 0.25 0.33 0.28 0.22

COEFFICIENT

OF EXPANSION,

α

8.1*10-

6/0K

17.5*10-

6/0K

0.9*10-

6/0K

5.4*10-

6/0K

Table 3.4.1 Properties of the candidate materials

3.5 Model Evaluation

It is very difficult to exactly model the brake Disc, in which there are still researches are

going on to find out transient thermo elastic behavior of Disc brake during braking applications.

There is always a need of some assumptions to model any complex geometry. These assumptions

are made, keeping in mind the difficulties involved in the theoretical calculation and the

importance of the parameters that are taken and those which are ignored. In modeling we always

ignore the things that are of less importance and have little impact on the analysis.

Due to the application of brakes on the car Disc brake rotor, heat generation takes place

due to friction and this thermal flux has to be conducted and dispersed across the Disc




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Rotor cross section. The condition of braking is very much severe and thus the thermal analysis

has to be carried out. The thermal loading as well as structure is axis-symmetric.Hence axis-

symmetric analysis can be performed, but in this study we performed 3-D analysis, which is an

exact representation for this thermal analysis. Thermal analysis is carried out and with the above

load structural analysis is also performed for analyzing the stability of the structure.

A model presents a three dimensional solid Disc squeezed by two finite-width friction

material called pads. The entire surface, S, of the Disc has three different regions including S1

and S2. On S1 heat flux is specified due to the frictional heating between the pads and Disc, and

S2 is defined for the convection boundary. The rest of the region, except S1 U S2, is either

temperature specified or assumed to be insulated: the inner and outer rim area of Disc.Since the

axis-symmetric model is considered all the nodes on the hub radius are fixed. So the nodal

displacements in the hub become zero i.e. in radial, axial and angular directions.

Figure 3.5.1 3-D Meshed Model Figure 3.5.2 Thermal Loading of

Brake Disc

In order to validate the present method, a comparison of transient results with the steady

state solution of thermo elastic behaviors was performed for the operation condition of the

constant hydraulic pressure P =10 MPa, μ=0.2 and angular velocity ù = 50 rad/s ( drag brake

application) during 4.5 seconds. If the transient solution for this operation condition converges to

the steady solution as time elapse, it can be regarded as validation of the applied transient scheme.

The thermal boundary conditions used are adiabatic on the boundary of the inner and outer radius




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and the prescribed temperature condition T = 20°C on the both boundaries along the radius of the

lower and upper pad by assumption of the cooling state.

3.6 Results and Discussion

The material properties and operation conditions used for the validation of the transient

thermo elastic scheme are given in Table No 4.2.The time step Δt =0005 sec. was used. The heat

flux distribution on the friction surfaces for the steady and transient (at t=5 sec) solution.

Actually, after time t=3 sec, a change of heat flux distribution does scarcely occur, and then the

steady state is reached. Also, this result indicates that the heat flux distribution on each friction

surface occur dissimilarly as time elapse. The major cause of these phenomena is that the contact

condition on the friction surfaces is changed to satisfy the new equilibrium state due to the rise in

temperature.In actually, variation of the rotating speed during braking must be determined

through vehicle dynamics. However, in this study, the rotating speed of Disc was considered to be

a known value.

The time history of hydraulic pressure h P and angular speed ù assumed for brake cycle is

shown. One cycle is composed of braking (4.5 sec), acceleration (10.5), and constant speed

driving (5 sec). In each process, the hydraulic pressure h P was assumed to linearly increase to 1

MPaby 1.5 sec and then kept constant until 4.5 sec. Also, the angular velocity ù was assumed to

linearly decay and finally became zero at 4.5 sec. The time step Δt =0.001 sec was used in the

computations. The material properties adopted in the computations are shown in Table. The

temperature distributions show high gradients near the region of friction surfaces and are almost

symmetric about the Disc’s mid plane at the early steps of brake application as shown. The

distribution of temperatures of the Disc brake is almost symmetrical about the Disc’s mid plane

and the Thermo Elastic Instability phenomenon does not occur during the braking process.




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Fig 3.6.1 Total Deformation of S2 Glass Disc Fig 3.6.2 Temperature Distribution in S2

Glass disc

Fig 3.6.3Temperature Distribution in S2 Glass Disc Fig 3.6.4Temperature Distribution in

EGlass Disc

The thermal expansion coefficient and the elastic modulus of pad materials have alarger

effect on the thermo elastic behaviors of Disc brakes. Therefore, the softer padimproves the

contact pressure distribution and results in a more even temperaturedistribution.In this section, the

transient thermo elastic analysis of the E-Glass and S2 glass fiber disc is performed for the drag

brake application (Ph = 1MPa, ù = 100 rad/s) for 4.5 s, andthen the results in the E-Glass and S2

glass fiber Discs (orthotropic case) are compared withthose using the material properties of CI

(isotropic case). Figures 6.9, 6.10 and 6.11 showsthe deformation, equivalent stress and

temperature distributions on the friction surfaces attime t = 1 and 4.5 s for the isotropic and

orthotropic material respectively. Compared with theisotropic case, the heat flux of the

orthotropic one are very uniformly distributed along thefriction surfaces and results in a more

even temperature distribution, namely, a thermo elasticstable state. These results show that the




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Disc brakes made of isotropic material can providebetter braking performance than the

orthotropic metal ones.

Material

Deformation Von-misses Stresses

(MPa)

Temperature

(°C)

mm max min max min

Cast

Iron 0.35191 50.334 0.92342 486.76 290.2

AlMMC 0.35229 211.98 2.7269 29.232 21.9

E-Glass 1.036 274.14 0.44893 1219.8 22.019

S2 Glass 0.16097 50.197 0.079753 66.137 11.867

Table 3.6.1 Comparison of the obtained results

Comparing the different results obtained from analysis in table 6.1. We found that themaximum

temperature rise in Cast Iron Disc is 486.76 º C, as shown in Figure, which ishigher than the

maximum temperature rise in S2 Glass fiber (66.137º C).The equivalentstresses induced at 66.137

º C in Cast Iron Disc is 50.3197 MPa as shown in Figure,which is within safe limit and less than

the equivalent stresses induced in all the other Discs.It is concluded that the S2 glass fiber brake

Disc the best possible combination for the presentBraking application.

3.7 E-Glass Brake Disc Model:

The Finite Element Analysis of the Brake discs of different materials shows that S2glass fiber is

suitable for braking application. Since S2 glass fibers are not readily available inthe market and

highly priced. Since the density of S2 Glass fibers and E-Glass fibers haveless difference, a model

of E-Glass fiber has been developed using the Hand layup process.Hand lay-up is the simplest

and oldest open molding method of the compositefabrication processes. It is a low volume, labor

intensive method suited especially for largecomponents, such as boat hulls. Glass fabric is




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positioned manually in the open mold, andresin is poured, brushed, or sprayed over and into the

glass plies. Entrapped air is removedmanually with squeegees or rollers to complete the laminates

structure. Room temperaturecuring polyesters and epoxies are the most commonly used matrix

resins. Curing is initiatedby a catalyst in the resin system, which hardens the fiber reinforced resin

composite withoutexternal heat. For a high quality part surface, a pigmented gel coat is first

applied to the moldsurface. The final E-glass brake disc model. The weight of this brake disc

model is800g, whereas the cast iron brakediscsweight 4.5 kgs. Thus brake disc models of low

weight and high strength have been developed using Hand Layup method.

Material Weight in kg

Cast Iron 3.450

E-Glass 1.020

Table 3.7.1 Weight Comparison

Fig 3.7.1 Final model of E-Glass fiber Brake disc Fig 3.7.2 Cast Iron Brake

Disc




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3.8 Conclusion:

In order to improve the braking efficiency and provide greater stability to vehicle

aninvestigation was carried out and the suitable hybrid composite material which is lighter

thancast iron and has good Young’s modulus, Yield strength and density properties. The

lowweight, the hardness, the stable characteristics also in case of high pressure and

temperatureand resistance to thermal shock.

The transient thermo elastic analysis of Disc brakes in repeated brake applications hasbeen

performed. ANSYS software is applied to the thermo elastic contact problem withfrictional heat

generation. To obtain the simulation of thermo elastic behavior appearing inDisc brakes, the

coupled heat conduction and elastic equations are solved with contactproblems. The effects of the

friction material properties on the contact ratio of frictionsurfaces are examined and the larger

influential properties are found to be the thermalexpansion coefficient and the elastic modulus. It

is observed that the orthotropic Disc brakescan provide better brake performance than the

isotropic ones because of uniform and mildpressure distributions. The present study can provide a

useful design tool and improve thebrake performance of Disc brake system. From Tablewe can

say that S2 glass fiber is thesuitable material for the braking operation and all the values obtained

from the analysis areless than their allowable values. Hence the brake Disc design is safe based on

the strengthand rigidity criteria.

References

1. Artus.S, Cocquempot, Staroswiecki.M, Hayat. S, Covo.C , (2004) , “TemperatureEstimation of

CHV Brake Discs using an Energy Balance Approach”, IEEEIntelligent Transportation Systems

Conference, Washington, D.C., USA,pp-390-395.

2. Artus.S, Cocquempot, Staroswiecki.M, Hayat. S, Covo.C,(2005), “CHV's brake

discstemperature estimation: results in open road Tests”, Proceedings of the 8th

International IEEE

Conference on Intelligent Transportation Systems Vienna, Austria.

3. Daniel Hochlenert, Thira Jearsiripongkul,(2006), “Disk Brake Squeal: Modeling andActive

Control”,IEEE transactions on RAM.




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August 2012

4. Fei Gao1, Gang Xiao, Yuanming Zhang, (2009), “Semi-similarity design ofmotorcycle-

hydraulic-disk brake: strategy and Application”, pp-576-579.

5. GuangqiangWu , Lin He ,XianjieMeng, (2009), “Numerical Study on the

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Disk Materials”, Department of Physics, University of Ulsan pp-680 – 749.




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12. Won Sun Chung, Sung Pil Jung “Numerical analysis method to estimate thermaldeformation

of a ventilated disc for automotives”.pp-40 –49

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Documents

TRANSIENT ANALYSIS OF ROTOR DISC OF DISC BRAKE USING ANSYS doc/IJMIE_AUGUST2012/IJMRA-MIE1626.pdf · TRANSIENT ANALYSIS OF ROTOR DISC OF DISC BRAKE USING ANSYS V.M.M.Thilak* _____